Linearizability Problem of Resonant Degenerate Singular Point for Polynomial Differential Systems
The linearizability (or isochronicity) problem is one of the open problems for polynomial differential systems which is far to be solved in general. A progressive way to find necessary conditions for linearizability is to compute period constants. In this paper, we are interested in the linearizabil...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/383282 |
| Summary: | The linearizability (or isochronicity) problem is one of the open problems for polynomial differential systems which is far to be solved in general. A progressive way
to find necessary conditions for linearizability is to compute period constants. In this
paper, we are interested in the linearizability problem of p : −q resonant degenerate
singular point for polynomial differential systems. Firstly, we transform degenerate
singular point into the origin via a homeomorphism. Moreover, we establish a new recursive algorithm to compute the so-called generalized period constants for the origin
of the transformed system. Finally, to illustrate the effectiveness of our algorithm, we
discuss the linearizability problems of 1 : −1 resonant degenerate singular point for a
septic system. We stress that similar results are hardly seen in published literatures
up till now. Our work is completely new and extends existing ones. |
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| ISSN: | 1110-757X 1687-0042 |